TY - GEN
T1 - Generalising and dualising the third list-homomorphism theorem
T2 - 16th ACM SIGPLAN International Conference on Functional Programming, ICFP'11
AU - Mu, Shin Cheng
AU - Morihata, Akimasa
PY - 2011/10/19
Y1 - 2011/10/19
N2 - The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl. We prove a dual theorem for unfolds and generalise both theorems to trees: if a function generating a list can be described both as an unfoldr and an unfoldl, the list can be generated from the middle, and a function that processes or builds a tree both upwards and downwards may independently process/build a subtree and its one-hole context. The point-free, relational formalism helps to reveal the beautiful symmetry hidden in the theorem.
AB - The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl. We prove a dual theorem for unfolds and generalise both theorems to trees: if a function generating a list can be described both as an unfoldr and an unfoldl, the list can be generated from the middle, and a function that processes or builds a tree both upwards and downwards may independently process/build a subtree and its one-hole context. The point-free, relational formalism helps to reveal the beautiful symmetry hidden in the theorem.
KW - Program derivation
KW - Third list homomorphism theorem
UR - http://www.scopus.com/inward/record.url?scp=80054060919&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80054060919&partnerID=8YFLogxK
U2 - 10.1145/2034773.2034824
DO - 10.1145/2034773.2034824
M3 - Conference contribution
AN - SCOPUS:80054060919
SN - 9781450308656
T3 - Proceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP
SP - 385
EP - 391
BT - ICFP'11 - Proceedings of the 2011 ACM SIGPLAN International Conference on Functional Programming
Y2 - 19 September 2011 through 21 September 2011
ER -